Aims & Learning Objectives:
Aims: To develop skills in the analysis of multivariate data and study the related theory.
Be able to carry out a preliminary analysis of multivariate data and select and apply an appropriate technique to look for structure in such data or achieve dimensionality reduction. Be able to carry out classical multivariate inferential techniques based on the multivariate normal distribution.
Introduction, Preliminary analysis of multivariate data.
Revision of relevant matrix algebra.
Principal components analysis: Derivation and interpretation; approximate reduction of dimensionality; scaling problems.
Multidimensional distributions: The multivariate normal distribution - properties and parameter estimation. One and two-sample tests on means, Hotelling's T-squared. Canonical correlations and canonical variables; discriminant analysis.
Topics selected from: Factor analysis. The multivariate linear model.
Metrics and similarity coefficients; multidimensional scaling.
Cluster analysis. Correspondence analysis. Classification and regression trees.